Hello, all. Digging though my last home assignment here, and stuck on2 problems once again. Here's the first one:

Prove that a^2 + b^2 + 1 > a + b + ab.

I'm considering two approaches. First one is to consider all cases:

When a and b are < 0, the statement is obviously true, since left sidewill always be >0 and right side will always be < 0When a and b are equal and are equal to 0, the left side is greater,since it has a constant.When a and b are equal and are equal to 1, both sides are the same, andthus the equation still holds.My only troubles are when a and b are between 0 and 1, and when theyare greater than one. Cannot find a proof without algebraicmanipulation.